"Her strength of conviction was recognised by her closest supporters and her strongest opponents," Ms Gillard said in a statement from China.

"I extend my sincere condolences and those of my fellow Australians to her family and friends."

Opposition Leader Tony Abbott was slightly more effusive in remembering Baroness Thatcher, who died at the age of 87 after months of poor health.

"Margaret Thatcher was one of the greatest British prime ministers and one of the most significant world leaders of our times," Mr Abbott said in a statement.

"She was the first female prime minister of Great Britain and ranks with the greatest of prime ministers because of the quality of her leadership and the impact she had on Britain and the wider world."

Mr Abbott said the conservative leader, known as The Iron Lady, was responsible for restoring Britain's place as a global powerhouse.

He said she gave Britons "renewed confidence" and ensured they "no longer simply dwelt on the glories of the past".

"The thoughts of the Coalition are with Baroness Thatcher's family and the British people at this time," he said.

Britain's first female PM Margaret Thatcher dies after stroke

Former British Prime Minister Margaret Thatcher has died following a stroke her spokesman Lord Bell said.

Lord Bell said: "It is with great sadness that Mark and Carol Thatcher announced that their mother Baroness Thatcher died peacefully following a stroke this morning.

"A further statement will be made later."

Buckingham Palace said Queen Elizabeth II was saddened by the news.

"The Queen was sad to hear the news of the death of Baroness Thatcher. Her Majesty will be sending a private message of sympathy to the family," the Palace said.

The former ruler suffered from dementia and has appeared rarely in public in recent years.

In a statement on the Downing Street Twitter feed, Prime Minister David Cameron said: "It was with great sadness that I learned of Lady Thatcher's death. We've lost a great leader, a great prime minister and a great Briton."

Politicians from across the political spectrum took to Twitter to pay tribute to Baroness Thatcher.

Tory MP Therese Coffey said the former Prime Minister had "transformed" the country, "putting Great back in Great Britain".

And UKIP leader Nigel Farage said she was a "great patriotic lady".

Labour MPs also paid tribute to Baroness Thatcher.

Shadow International Development Secretary Ivan Lewis said: "Hoping all Labour supporters will respond with dignity + respect to news of Baroness Thatcher's death. Our thoughts with her family + friends."

And former Labour minister and MP Tony McNulty tweeted: "God bless her and thoughts are with her family. RIP."

Baroness Thatcher was Conservative prime minister from 1979 to 1990. She was the first woman to hold the post.

Born Margaret Roberts in Grantham in 1925 she went on to become the Conservative MP for Finchley, north London in 1959.

She subsequently became Education Secretary before successfully challenging former prime minister Edward Heath for her party's leadership in 1975.

Thatcher was the longest-serving (1979-1990) Prime Minister of the United Kingdom of the 20th century, and the only woman ever to have held the post.

A Soviet journalist called her the "Iron Lady", a nickname which became associated with her uncompromising politics and leadership style.

As Prime Minister, she implemented Conservative policies that have come to be known as Thatcherism.

Originally a research chemist before becoming a barrister, Thatcher was elected Member of Parliament (MP) for Finchley in 1959.

Edward Heath appointed her Secretary of State for Education and Science in his 1970 government.

In 1975 Thatcher defeated Heath in the Conservative Party leadership election and became Leader of the Opposition, as well as the first woman to lead a major political party in the United Kingdom.

She became Prime Minister after winning the 1979 general election.

After entering 10 Downing Street, Thatcher introduced a series of political and economic initiatives to reverse what she perceived to be Britain's precipitous national decline.

Her political philosophy and economic policies emphasised deregulation (particularly of the financial sector), flexible labour markets, the privatisation of state-owned companies, and reducing the power and influence of trade unions.

Thatcher's popularity during her first years in office waned amid recession and high unemployment, until economic recovery and the 1982 Falklands War brought a resurgence of support, resulting in her re-election in 1983.

Thatcher was re-elected for a third term in 1987, but her Community Charge (popularly referred to as "poll tax") was widely unpopular and her views on the European Community were not shared by others in her Cabinet.

She resigned as Prime Minister and party leader in November 1990, after Michael Heseltine launched a challenge to her leadership.

Thatcher held a life peerage as Baroness Thatcher, of Kesteven in the County of Lincolnshire, which entitled her to sit in the House of Lords.

She retired from the Commons in 1992.

A selection of Baroness Thatcher's best quotes:

1."Being powerful is like being a lady. If you have to tell people you are, you aren't."

2."I always cheer up immensely if an attack is particularly wounding because I think, well, if they attack one personally, it means they have not a single political argument left."

3."I am extraordinarily patient, provided I get my own way in the end."

4."If you want something said, ask a man; if you want something done, ask a woman."

5."Any woman who understands the problems of running a home will be nearer to understanding the problems of running a country."

6."A world without nuclear weapons would be less stable and more dangerous for all of us."

7."To wear your heart on your sleeve isn't a very good plan; you should wear it inside, where it functions best."

8."I seem to smell the stench of appeasement in the air."

9."I don't mind how much my ministers talk, as long as they do what I say."

10."Pennies don't fall from heaven; they have to be earned here on Earth."